User:Mpagey/Padmakar-Ivan Index

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Consider a graph, $G$ , such that the edge connecting any two given points, $u$ and $v$ , in $G$ is denoted as $e$ . Let $n_{eu}(e|G)$ represent the number of edges of $G$ that are closer to point $u$ than point $v$ . Similarly, let $n_{ev}(e|G)$ represent the number of edges of $G$ that are closer to $v$ than $u$ . In this case, the Padmakar-Ivan Index of the graph $G$ , $PI(G)$ , is defined as: $PI(G)=\sum _{\forall {e}}\left(n_{eu}(e|G)+n_{ev}(e|G)\right)$

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Category:Graph_theory